Question

Solve: $\int \frac{\log (1+x)}{1+x}dx$

Answer 1

$\int \frac{log(1+x)}{1+x}dx$

Put $log(1+x)=t$

Differentiating $\frac{1}{1+x}dx=dt$

$\int t\cdot dt$

$=\left[\frac{t^2}{2}\right]+c$

$=\frac{\left(log\right(1+x){]}^2}{2}+c$.